While the world is watching and waiting with bated breath after Baby Boy Cambridge's birth, two VIP guests managed to sneak some special one-on-one time with Kate and Will's tiny bundle of joy on Tuesday, July 23: Kate's parents Carole and Michael Middleton.

The proud grandparents arrived at the Lindo Wing of St. Mary's Hospital at approximately 3:04 p.m. London time to visit their daughter and her newborn son. The couple arrived in a black taxi and was escorted into the building; acknowledging photographers briefly before meeting the little prince, both first-time grandparents beamed.

Neither Carole nor Michael (nor Kate's younger sister Pippa) were present at the birth of the royal baby, despite initial rumors that the Middleton women would be in the delivery room for the highly anticipated birth.

"Buckingham Palace denied rumors that they were going to be in the delivery room with Kate," NBC News reported on Monday. "She very much wants just her husband to be there."

On Tuesday, the first-time parents released a joint statement thanking the hospital for their "tremendous care" in helping to make the delivery a smooth one.

"We would like to thank the staff at the Lindo Wing and the whole hospital for the tremendous care the three of us have received," they said in a statement. "We know it has been a very busy period for the hospital and we would like to thank everyone -- staff, patients, and visitors -- for the understanding during this time."